Fast marching methods for the continuous traveling salesman problem

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We consider a problem in which we are given a domain, a cost function which depends on position at each point in the domain, and a subset of points ('cities') in the domain. The goal is to determine the cheapest closed path that visits each city in the domain once. This can be thought of as a version of the Traveling Salesman Problem, in which an underlying known metric determines the cost of moving through each point of the domain, but in which the actual shortest path between cities is unknown at the outset. We describe algorithms for both a ... continued below

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Andrews, J. & Sethian, J.A. December 1, 2008.

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We consider a problem in which we are given a domain, a cost function which depends on position at each point in the domain, and a subset of points ('cities') in the domain. The goal is to determine the cheapest closed path that visits each city in the domain once. This can be thought of as a version of the Traveling Salesman Problem, in which an underlying known metric determines the cost of moving through each point of the domain, but in which the actual shortest path between cities is unknown at the outset. We describe algorithms for both a heuristic and an optimal solution to this problem. The order of the heuristic algorithm is at worst case M * N logN, where M is the number of cities, and N the size of the computational mesh used to approximate the solutions to the shortest paths problems. The average runtime of the heuristic algorithm is linear in the number of cities and O(N log N) in the size N of the mesh.

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  • Journal Name: Proceedings of the National Academy of Sciences

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  • Report No.: LBNL-1313E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 945046
  • Archival Resource Key: ark:/67531/metadc900305

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  • December 1, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:18 p.m.

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Andrews, J. & Sethian, J.A. Fast marching methods for the continuous traveling salesman problem, article, December 1, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc900305/: accessed September 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.